2020-01 Another singular matrix

For a given positive integer \( n \), find all non-negative integers \( r \) such that the following statement holds:

For any real \( n \times n \) matrix \( A \) with rank \( r \), there exists a real \( n \times n \) matrix \( B \) such that \( \det (AB+BA) \neq 0 \).

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2020-01 Another singular matrix, 4.3 out of 5 based on 3 ratings

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